In an isosceles trapezium, the lateral side is 10, the larger base is 14, the smaller one is 4

In an isosceles trapezium, the lateral side is 10, the larger base is 14, the smaller one is 4, and the angle for the smaller base is 120º. Find the area of the trapezoid.

Let us omit the height of the CH trapezoid and determine the angles of the formed right-angled triangle CDH.

The angle DСН = ВСD – ВСН = 120 – 90 = 30, then the leg DН lies against it, and its length is: DН = СD / 2 = 10/2 = 5 cm.

Let’s calculate the length of CH as the leg of a right-angled triangle CDH.

CH ^ 2 = CD ^ 2 – DH ^ 2 = 100 – 25 = 75.

CH = 5 * √3 cm.

Determine the area of the trapezoid.

Savsd = (ВС + АD) * СН / 2 = (4 + 14) * 5 * √3 / 2 = 45 * √3 cm2.

Answer: The area of the trapezoid is 45 * √3 cm2.